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Existence and approximation results to the Cauchy problem for a class of differential-algebraic equations. (English) Zbl 0772.34003

Summary: For a class of differential-algebraic equations arising for example in modelling electrical circuits conditions are derived which ensure the existence of a unique solution of the Cauchy problem on any finite interval and its computation by means of a wave form relaxation algorithm in case of a large system. The solution concepts is understood in the sense of Carathéodory.

MSC:

34A09 Implicit ordinary differential equations, differential-algebraic equations
34A34 Nonlinear ordinary differential equations and systems
65J99 Numerical analysis in abstract spaces
94C05 Analytic circuit theory
65L05 Numerical methods for initial value problems involving ordinary differential equations
37-XX Dynamical systems and ergodic theory
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